Integral of $$$\frac{\sqrt[3]{x + 2} + \sqrt{x + 2}}{\sqrt[4]{x + 6}}$$$

The calculator will find the integral/antiderivative of $$$\frac{\sqrt[3]{x + 2} + \sqrt{x + 2}}{\sqrt[4]{x + 6}}$$$, with steps shown.

Find $$$\int \frac{\sqrt[3]{x + 2} + \sqrt{x + 2}}{\sqrt[4]{x + 6}}\, dx$$$.